arXiv subjects

Nicolas Vayatis

Publications and source records attributed to Nicolas Vayatis.

At least 55 records · Page 3Linked to original sources

arXiv2019

Revealing posturographic features associated with the risk of falling in patients with Parkinsonian syndromes via machine learning

Falling in Parkinsonian syndromes (PS) is associated with postural instability and consists a common cause of disability among PS patients. Current posturographic practices record the body's center-of-pressure displacement (statokinesigram) while the patient stands on a force platform. Statokinesigrams, after appropriate signal processing, can offer numerous posturographic features, which however challenges the efforts for valid statistics via standard univariate approaches. In this work, we present the ts-AUC, a non-parametric multivariate two-sample test, which we employ to analyze statokinesigram differences among PS patients that are fallers (PSf) and non-fallers (PSNF). We included 123 PS patients who were classified into PSF or PSNF based on clinical assessment and underwent simple Romberg Test (eyes open/eyes closed). We analyzed posturographic features using both multiple testing with p-value adjustment and the ts-AUC. While the ts-AUC showed significant difference between groups (p-value = 0.01), multiple testing did not show any such difference. Interestingly, significant difference between the two groups was found only using the open-eyes protocol. PSF showed significantly increased antero-posterior movements as well as increased posturographic area, compared to PSNF. Our study demonstrates the superiority of the ts-AUC test compared to standard statistical tools in distinguishing PSF and PSNF in the multidimensional feature space. This result highlights more generally the fact that machine learning-based statistical tests can be seen as a natural extension of classical statistical approaches and should be considered, especially when dealing with multifactorial assessments.

cs.LG↗

arXiv2018

DICOD: Distributed Convolutional Sparse Coding

In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it communication efficient. It is based on coordinate descent and uses locally greedy updates which accelerate the resolution compared to greedy coordinate selection. We prove the convergence of this algorithm and highlight its computational speed-up which is super-linear in the number of cores used. We also provide empirical evidence for the acceleration properties of our algorithm compared to state-of-the-art methods.

cs.LG↗

arXiv2018

ruptures: change point detection in Python

ruptures is a Python library for offline change point detection. This package provides methods for the analysis and segmentation of non-stationary signals. Implemented algorithms include exact and approximate detection for various parametric and non-parametric models. ruptures focuses on ease of use by providing a well-documented and consistent interface. In addition, thanks to its modular structure, different algorithms and models can be connected and extended within this package.

stat.CO↗

arXiv2017

A Spectral Method for Activity Shaping in Continuous-Time Information Cascades

Information Cascades Model captures dynamical properties of user activity in a social network. In this work, we develop a novel framework for activity shaping under the Continuous-Time Information Cascades Model which allows the administrator for local control actions by allocating targeted resources that can alter the spread of the process. Our framework employs the optimization of the spectral radius of the Hazard matrix, a quantity that has been shown to drive the maximum influence in a network, while enjoying a simple convex relaxation when used to minimize the influence of the cascade. In addition, use-cases such as quarantine and node immunization are discussed to highlight the generality of the proposed activity shaping framework. Finally, we present the NetShape influence minimization method which is compared favorably to baseline and state-of-the-art approaches through simulations on real social networks.

stat.ML↗

arXiv2017

Global optimization of Lipschitz functions

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO which assumes the Lipschitz constant to be known. Consistency, minimax rates for LIPO are proved, as well as fast rates under an additional Hölder like condition. An adaptive version of LIPO is also introduced for the more realistic setup where the Lipschitz constant is unknown and has to be estimated along with the optimization. Similar theoretical guarantees are shown to hold for the adaptive LIPO algorithm and a numerical assessment is provided at the end of the paper to illustrate the potential of this strategy with respect to state-of-the-art methods over typical benchmark problems for global optimization.

stat.ML↗

arXiv2017

A ranking approach to global optimization

We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking rule of f. Based on this idea, we relate global optimization to bipartite ranking which allows to address problems with high dimensional input space, as well as cases of functions with weak regularity properties. The paper introduces novel meta-algorithms for global optimization which rely on the choice of any bipartite ranking method. Theoretical properties are provided as well as convergence guarantees and equivalences between various optimization methods are obtained as a by-product. Eventually, numerical evidence is given to show that the main algorithm of the paper which adapts empirically to the underlying ranking structure essentially outperforms existing state-of-the-art global optimization algorithms in typical benchmarks.

stat.ML↗

arXiv2016

Spectral Bounds in Random Graphs Applied to Spreading Phenomena and Percolation

In this paper, we derive nonasymptotic theoretical bounds for the influence in random graphs that depend on the spectral radius of a particular matrix, called the Hazard matrix. We also show that these results are generic and valid for a large class of random graphs displaying correlation at a local scale, called the LPC random graphs. In particular, they lead to tight and novel bounds in percolation, epidemiology and information cascades. The main result of the paper states that the influence in the sub-critical regime for LPC random graphs is at most of the order of $O(\sqrt{n})$ where $n$ is the size of the network, and of $O(n^{2/3})$ in the critical regime, where the epidemic thresholds are driven by the size of the spectral radius of the Hazard matrix with respect to 1. As a corollary, it is also shown that such bounds hold for the size of the giant component in inhomogeneous percolation, the SIR model in epidemiology, as well as for the long-term influence of a node in the Independent Cascade Model.

math.PR↗

arXiv2016

Stochastic Process Bandits: Upper Confidence Bounds Algorithms via Generic Chaining

The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his operability over a continuous domain. The theoretical framework applies to functions under weak probabilistic smoothness assumptions and also extends significantly the spectrum of application of UCB strategies. Moreover generic regret bounds are derived which are then specialized to Gaussian processes indexed on infinite-dimensional spaces as well as to quadratic forms of Gaussian processes. Lower bounds are also proved in the case of Gaussian processes to assess the optimality of the proposed algorithm.

stat.ML↗

arXiv2015

Optimization for Gaussian Processes via Chaining

In this paper, we consider the problem of stochastic optimization under a bandit feedback model. We generalize the GP-UCB algorithm [Srinivas and al., 2012] to arbitrary kernels and search spaces. To do so, we use a notion of localized chaining to control the supremum of a Gaussian process, and provide a novel optimization scheme based on the computation of covering numbers. The theoretical bounds we obtain on the cumulative regret are more generic and present the same convergence rates as the GP-UCB algorithm. Finally, the algorithm is shown to be empirically more efficient than its natural competitors on simple and complex input spaces.

stat.ML↗

arXiv2015

Gaussian Process Optimization with Mutual Information

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian Process Mutual Information algorithm (GP-MI), which significantly improves further these upper bounds for the cumulative regret. We confirm the efficiency of this algorithm on synthetic and real tasks against the natural competitor, GP-UCB, and also the Expected Improvement heuristic.

stat.ML↗

arXiv2014

Tight Bounds for Influence in Diffusion Networks and Application to Bond Percolation and Epidemiology

In this paper, we derive theoretical bounds for the long-term influence of a node in an Independent Cascade Model (ICM). We relate these bounds to the spectral radius of a particular matrix and show that the behavior is sub-critical when this spectral radius is lower than $1$. More specifically, we point out that, in general networks, the sub-critical regime behaves in $O(\sqrt{n})$ where $n$ is the size of the network, and that this upper bound is met for star-shaped networks. We apply our results to epidemiology and percolation on arbitrary networks, and derive a bound for the critical value beyond which a giant connected component arises. Finally, we show empirically the tightness of our bounds for a large family of networks.

math.PR↗

arXiv2014

What Makes a Good Plan? An Efficient Planning Approach to Control Diffusion Processes in Networks

In this paper, we analyze the quality of a large class of simple dynamic resource allocation (DRA) strategies which we name priority planning. Their aim is to control an undesired diffusion process by distributing resources to the contagious nodes of the network according to a predefined priority-order. In our analysis, we reduce the DRA problem to the linear arrangement of the nodes of the network. Under this perspective, we shed light on the role of a fundamental characteristic of this arrangement, the maximum cutwidth, for assessing the quality of any priority planning strategy. Our theoretical analysis validates the role of the maximum cutwidth by deriving bounds for the extinction time of the diffusion process. Finally, using the results of our analysis, we propose a novel and efficient DRA strategy, called Maximum Cutwidth Minimization, that outperforms other competing strategies in our simulations.

math.OC↗

arXiv2014

Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes

In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on nonparametric learning and propose a novel algorithm called MEMIP (Markovian Estimation of Mutually Interacting Processes) that makes use of polynomial approximation theory and self-concordant analysis in order to learn both triggering kernels and base intensities of events. Moreover, considering that N historical observations are available, the algorithm performs log-likelihood maximization in $O(N)$ operations, while the complexity of non-Markovian methods is in $O(N^{2})$. Numerical experiments on simulated data, as well as real-world data, show that our method enjoys improved prediction performance when compared to state-of-the art methods like MMEL and exponential kernels.

math.PR↗

arXiv2013

Sloshing in the LNG shipping industry: risk modelling through multivariate heavy-tail analysis

In the liquefied natural gas (LNG) shipping industry, the phenomenon of sloshing can lead to the occurrence of very high pressures in the tanks of the vessel. The issue of modelling or estimating the probability of the simultaneous occurrence of such extremal pressures is now crucial from the risk assessment point of view. In this paper, heavy-tail modelling, widely used as a conservative approach to risk assessment and corresponding to a worst-case risk analysis, is applied to the study of sloshing. Multivariate heavy-tailed distributions are considered, with Sloshing pressures investigated by means of small-scale replica tanks instrumented with d >1 sensors. When attempting to fit such nonparametric statistical models, one naturally faces computational issues inherent in the phenomenon of dimensionality. The primary purpose of this article is to overcome this barrier by introducing a novel methodology. For d-dimensional heavy-tailed distributions, the structure of extremal dependence is entirely characterised by the angular measure, a positive measure on the intersection of a sphere with the positive orthant in Rd. As d increases, the mutual extremal dependence between variables becomes difficult to assess. Based on a spectral clustering approach, we show here how a low dimensional approximation to the angular measure may be found. The nonparametric method proposed for model sloshing has been successfully applied to pressure data. The parsimonious representation thus obtained proves to be very convenient for the simulation of multivariate heavy-tailed distributions, allowing for the implementation of Monte-Carlo simulation schemes in estimating the probability of failure. Besides confirming its performance on artificial data, the methodology has been implemented on a real data set specifically collected for risk assessment of sloshing in the LNG shipping industry.

math.ST↗

arXiv2013

Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration

In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function can be evaluated in parallel with batches of fixed size and analyze the benefit compared to the purely sequential procedure in terms of cumulative regret. We introduce the Gaussian Process Upper Confidence Bound and Pure Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations. We prove theoretical upper bounds on the regret with batches of size K for this procedure which show the improvement of the order of sqrt{K} for fixed iteration cost over purely sequential versions. Moreover, the multiplicative constants involved have the property of being dimension-free. We also confirm empirically the efficiency of GP-UCB-PE on real and synthetic problems compared to state-of-the-art competitors.

cs.LG↗

arXiv2013

Can Small Islands Protect Nearby Coasts From Tsunamis? An Active Experimental Design Approach

Small islands in the vicinity of the mainland are believed to offer protection from wind and waves and thus coastal communities have been developed in these areas. However, what happens when it comes to tsunamis is not clear. Will these islands act as natural barriers ? Recent post-tsunami survey data, supported by numerical simulations, reveal that the run-up on coastal areas behind small islands was significantly higher than on neighboring locations not affected by the presence of the island. To study the conditions of this run- up amplification, we solve numerically the nonlinear shallow water equations (NSWE). We use the simplified geometry of a conical island sitting on a flat bed in front of a uniform sloping beach. By doing so, the experimental setup is defined by five physical parameters, namely the island slope, the beach slope, the water depth, the distance between the island and the plane beach and the incoming wavelength, while the wave height was kept fixed. The objective is twofold: Find the maximum run-up amplification with the least number of simulations. To achieve this goal, we build an emulator based on Gaussian Processes to guide the selection of the query points in the parameter space.

physics.flu-dyn↗

arXiv2012

Link Prediction in Graphs with Autoregressive Features

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into account both sparsity and low rank properties of the matrices. Oracle inequalities are derived and illustrate the trade-offs in the choice of smoothing parameters when modeling the joint effect of sparsity and low rank property. The estimate is computed efficiently using proximal methods through a generalized forward-backward agorithm.

stat.ML↗

arXiv2012

Estimation of Simultaneously Sparse and Low Rank Matrices

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce a convex mixed penalty which involves $\ell_1$-norm and trace norm simultaneously. We obtain an oracle inequality which indicates how the two effects interact according to the nature of the target matrix. We bound generalization error in the link prediction problem. We also develop proximal descent strategies to solve the optimization problem efficiently and evaluate performance on synthetic and real data sets.

cs.DS↗